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cater- +‎ corner, where cater- is of disputed origin. Liberman argues that this is a prefix meaning “crooked, angled, clumsy”, of North Germanic origin; compare cater-cousin.[1] The verb cater ‎(“move diagonally, place diagonally, cut diagonally”) is attested from 1577 (Liberman proposes this as a backformation from cater-), and in 19th century Lancashire dialect, cater-cornered refers both to stone blocks that are out of square, and people who walk twisted (with one side in front of the other), especially if partially paralyzed.[1] Further awkward and clumsy are of Scandinavian origin, and Old Irish cittach ‎(“left-handed, awkward”) is cognate to cater- words, also suggesting a Scandinavian origin.

A commonly proposed etymology (proposed in the 19th century) derives cater, from Frenchquatre ‎(“four”) (hence “four corner” – at the opposite corner of a square), and similarly cater-cousin from “fourth cousin”, while Liberman rejects this as implausible – similar terms from French are simply calqued as “four corners” (as in “four corners of the world”, from French “les quatre coins du monde”), the English term cater ‎(“four”) (from French) was primarily used in dice, the domestication of a specialized foreign term as an adverb for “across” seems implausible, there are many Germanic terms that appear to be cognates, and other terms with cater- are found in English dialects.[1]

caterpillar and caterwaul are unrelated (derived from cognates to cat), but may have influenced the pronunciation of earlier *cate- (later cater-), or undergone similar sound changes.[1]

Various corruptions exist, replacing unfamiliar cater with words related to cat (catty, kitty). An almost identical process occurred in Germanic, with many place names have Kat or similar components, which are not plausible due to relationships with cats (German Katze), but rather are ascribed as due to being crooked, in a corner, or otherwise curved.[1]